The widespread deployment of wireless networks presents an opportunity for localization and mapping using signal-strength measurements. Wireless networks are ubiquitous, whether in the home, office, shopping malls, or airports.
Recent work in signal-strength-based simultaneous localization and mapping (SLAM) uses Gaussian process latent variable models (GP-LVM). This work, however, requires that maps are limited to very specific predefined shapes (e.g. narrow and straight hallways) and WIFI fingerprints are assumed unique at distinct locations. Generally, in the absence of any odometry information, arbitrary assumptions must be made about human walking patterns and data association.
GraphSLAM is a technique used in the robotics community for simultaneously estimating a trajectory and building a map offline. It shares many benefits of Gaussian processes, but can be applied to a broader range of environments. Below, it is shown how wireless signal strength SLAM can be formulated as a GraphSLAM problem. By using GraphSLAM, limitations of traditional approaches are addressed to improve runtime complexity from O(N3) to O(N2) where N is the dimensionality of the state space, i.e., the number of poses being estimated.
In both GraphSLAM and Gaussian processes, measurement likelihoods are modeled as Gaussian random variables. Gaussian processes can improve their model fit by moving points away from each other. To prevent these trivial solutions, GP-LVM methods require special constraints. In the case of signal strength SLAM, the special constraints force similar signal strengths to similar locations. GraphSLAM requires no special constraints. This makes GraphSLAM suitable to a wider range of real-world environments.
An appeal of GraphSLAM is that it reduces to a standard non-linear least squares problem. This gives GraphSLAM access to widely used and well-studied techniques for its optimization. A parameterization of the state space for typical mobile phone applications is presented below.
If wireless signal strength maps are determined ahead of time, Monte Carlo localization methods can achieve high accuracy indoor localization. In a traditional approach, the signal strength map is discretized into a spatial grid and, combined with contact sensing, obtains 0.25 m accuracy using standard Monte Carlo methods while improving convergence time over contact sensing alone. In another approach, spatial discretization of the signal strength map is performed and combine with WIFI with a low-cost image sensor to localize within 3 m. In traditional approaches, however, the process for obtaining signal strength maps is expensive and time consuming.
Outdoor applications have been handled by GPS and/or attenuation model or range-based SLAM methods. Other indoor signal-strength-based localization research relies on extensive training phases or incorporates other features of the signal such as time-of-arrival or angle-of-arrival measurements. In most pedestrian applications, however, such data is inaccessible to the general public without additional infrastructure costs. The implications of low-cost signal-strength SLAM are especially meaningful for large (indoor) GPS deprived environments such as shopping malls, airports, etc. where wireless internet infrastructure is readily accessible.
Existing wireless mapping techniques model the signal data in different ways. Some traditional techniques assume a model of the signal propagation. Other use a connectivity graph of predetermined cells to localize coarsely. Since these techniques rely on pre-existing information about the environment, they do not handle the problem of mapping in unknown locations.
The current state of the art uses Gaussian processes to determine a map of signal strength without modeling the propagation from transmitting nodes explicitly. Gaussian processes are applied to WiFi-SLAM under a specific set of assumptions.